Nonlinear equations with superposition formulas and the exceptional group G2. II. Classification of the equations

DOI10.1063/1.527636zbMath0614.22009OpenAlexW2013357563MaRDI QIDQ4722272

Véronique Hussin, Pavel Winternitz, Jules Beckers

Publication date: 1987

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.527636

zbMATH Keywords

homogeneous spacesexceptional Lie groupisotropy groupmaximal parabolic subgroupssuperposition formulas\(G_ 2\)semisimple subgroups

Mathematics Subject Classification ID

Supersymmetric field theories in quantum mechanics (81T60) Nonlinear differential equations in abstract spaces (34G20) Exceptional (super)algebras (17B25) Analysis on real and complex Lie groups (22E30) Applications of Lie groups to the sciences; explicit representations (22E70) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65)

Related Items (5)

Rotations in the space of Split octonions ⋮ Nonlinear equations with superposition formulas and exceptional group G2. III. The superposition formulas ⋮ Quaternionic Kähler manifolds, constrained instantons and the magic square. I. ⋮ Superposition formulas for nonlinear superequations ⋮ Nonlinear superposition formulas based on imprimitive group action

Cites Work

• Bäcklund transformations for nonlinear sigma models with values in Riemannian symmetric spaces
• Systems of ordinary differential equations with nonlinear superposition principles
• Complex parabolic subgroups of \(G_ 2\) and nonlinear differential equations
• A nonlinear superposition principle admitted by coupled Riccati equations of the projective type
• Classification of systems of nonlinear ordinary differential equations with superposition principles
• Superposition laws for solutions of differential matrix Riccati equations arising in control theory
• Simple subgroups of simple Lie groups and nonlinear differential equations with superposition principles
• Tensor fields invariant under subgroups of the conformal group of space-time
• Nonlinear equations with superposition formulas and the exceptional group G2. I. Complex and real forms of g2 and their maximal subalgebras

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